A ball is projected horizontally from the top of a building, as shown in Fig. 2.1. The ball has a horizontal speed of $8.2\,\text{m s}^{-1}$. The building’s side is vertical. At point $P$ on the ball’s path, the ball is distance $x$ from the building and is travelling at an angle of $60^\circ$ to the horizontal. Air resistance is negligible.
(a(i))[2]
For the ball at point $P$, show that its vertical component of velocity is $14.2\,\text{m s}^{-1}$.
(a(ii))[2]
Find the vertical distance the ball has descended.
(a(iii))[2]
Find the horizontal distance $x$.
(b)[4]
The path of the ball in (a), with an initial horizontal speed of $8.2\,\text{m s}^{-1}$, is shown again in Fig. 2.2. On Fig. 2.2, sketch the revised path for a ball with initial horizontal speed (i) greater than $8.2\,\text{m s}^{-1}$ and negligible air resistance (label this path G), (ii) equal to $8.2\,\text{m s}^{-1}$ but with air resistance acting (label this path A).
(b(i))[2]
Greater than $8.2\,\text{m s}^{-1}$, with negligible air resistance, and label this path G.
(b(ii))[2]
Equal to $8.2\,\text{m s}^{-1}$, but with air resistance, and label this path A.
Worked solution & mark scheme
This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The horizontal speed stays constant at $8.2\,\mathrm{m\,s^{-1}}$” …